Finite $p$-supersoluble groups with some $E$-$S$-supplemented subgroups

Abstract

Let $H$ be a subgroup of a group $G$ and $H_{eG}$ denote the subgroup of $H$ generated by all those subgroups of $H$ which are $S$-permutably embedded in $G$. $H$ is said to be $E$-$S$-supplemented in $G$ if there exists a subnormal subgroup $T$ of $G$ such that $G=HT$ and $H\cap T\le H_{eG}$. In this paper, we investigate the influence of some $E$-$S$-supplemented subgroups on the structure of finite group. Some new characterizations of $p$-supersoluble groups are obtained.